Local rigidity of higher rank partially hyperbolic algebraic actions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2011
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| _version_ | 1866908273703124992 |
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| author | Wang, Zhenqi Jenny |
| author_facet | Wang, Zhenqi Jenny |
| contents | We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C^\infty$ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric space examples and automorphisms on nilmanifolds. The method is a combination of representation theory, harmonic analysis and a KAM iteration. A striking feature of the method is no specific information from representation theory is needed. It is the first time local rigidity for non-accessible partially hyperbolic actions has ever been obtained other than torus examples. Even for Anosov actions, our results are new: it is the first time twisted spaces with non-abelian nilradical have been treated in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1103_3077 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Local rigidity of higher rank partially hyperbolic algebraic actions Wang, Zhenqi Jenny Dynamical Systems We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C^\infty$ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric space examples and automorphisms on nilmanifolds. The method is a combination of representation theory, harmonic analysis and a KAM iteration. A striking feature of the method is no specific information from representation theory is needed. It is the first time local rigidity for non-accessible partially hyperbolic actions has ever been obtained other than torus examples. Even for Anosov actions, our results are new: it is the first time twisted spaces with non-abelian nilradical have been treated in the literature. |
| title | Local rigidity of higher rank partially hyperbolic algebraic actions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/1103.3077 |